The company now says it will leave the issue to politicians

After the chain’s president, Dan Cathy, told an interviewer that the restaurant’s management resolutely objected to gay marriage and could only support “the biblical definition of the family unit,” other companies and public officials quickly moved to distance themselves from the chain, the Los Angeles Times notes.

Boston Mayor Thomas Menino promised to block any attempt by the chain to open a restaurant in his city.

The Jim Henson Company, which owns the Muppets, said that it will donate the payments it has received from a children’s meal partnership with Chick-fil-A to a gay and lesbian advocacy group and would not pursue any further projects with the chain.

An online petition calling for a boycott of Chick-fil-A has gained 4,000 signatures. And prominent celebrities have taken to Twitter to denounce the chicken-sandwich chain.

Perhaps stung by the criticism, Chick-fil-A said late last week that it would not make any further statements on the subject of gay marriage.

Still, Chick-fil-A’s stand has attracted support from conservative figures including former Arkansas Governor Mike Huckabee, who hosts a TV show on News Corp.’s (NASDAQ:NWSA) FOX News.

Huckabee defended the company from its detractors and has dubbed August 1, “Chick-fil-A Appreciation Day.”